First slide

Dynamics of rotational motion about fixed axis

Question

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder, if the rope is pulled with a force of 30 N? [NEET 2017]

Moderate

A

25 ${ms}^{- 2}$
B

0.25 rad $s^{- 2}$
C

25 rad $s^{- 2}$
D

5 ${ms}^{- 2}$

Solution

Torque ( $τ$ ) acting on a body and angular acceleration ( $α$ ) produced in it are related as
$τ$ = I $α$
Consider a hollow cylinder around which a rope is wounded.
Torque acting on the cylinder due to the force F is $τ = F r .$
Now, we have $τ$ = I $α$
where, I = moment of inertia of the cylinder about the axis through the centre.
$\Rightarrow I = m r^{2}$
Given, $F = 30 N, m = 3 kg and r = 40 cm = 40 \times 10^{- 2} m$
Angular acceleration,
$α = \frac{τ}{I} = \frac{F r}{m r^{2}}$
$= \frac{F}{m r} = \frac{30}{3 \times 40 \times 10^{- 2}}$
$= \frac{100}{4} = 25 {rads}^{- 2}$

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